Let be defined by

MATHEMATICS · Subjective · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let q:(−3,3]→Rq:(-3,3]\to\mathbb R be defined by q(x)=⌊x+1⌋−sgn⁡(x)q(x)=\lfloor x+1\rfloor-\operatorname{sgn}(x). Determine the range of qq.

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